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#1 2013-04-05 02:40:26

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Bayes' theorem problem

The probability that Katarina will correctly solve a given math problem is 1/8. The probability that Layla will solve the same problem correctly is 1/12. Given that they are both incorrect, the probability that they will give the same incorrect numerical result is 1/1001.

Suppose Katarina and Layla solve a math problem independently and get the same numerical result. The probability that they get the correct answer, given that they got the same numerical result, can be written as a/b, where a and b are cop-rime positive integers. Find a+b.


Clarification: When both of them solve the question correctly, they got the same numerical result.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2013-04-05 03:02:58

gAr
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Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

Is it 2098?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#3 2013-04-05 03:13:51

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Bayes' theorem problem

There's another clue which says that the answer is within 0 to 999 inclusive


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#4 2013-04-05 03:49:33

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

The probability that they get the correct answer, given that they got the same numerical result

Should that be same incorrect numerical result?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-04-05 03:55:01

gAr
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Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

I can't think of any other answer.

Hi bobbym,

Yeah, in that case we can have a zero!

Last edited by gAr (2013-04-05 04:00:49)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#6 2013-04-05 04:20:53

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,211
Website

Re: Bayes' theorem problem

Hi;


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#7 2013-04-05 04:31:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Hi Agnishom;

I am getting 79?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8 2013-04-05 04:36:33

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,211
Website

Re: Bayes' theorem problem

They tell its wrong.

I wanted to attach an image to post #6, for some reason i couldn't


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#9 2013-04-05 04:42:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Was it too big?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#10 2013-04-05 04:49:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,211
Website

Re: Bayes' theorem problem

I try again

View Image: image.jpg

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#11 2013-04-05 04:58:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Hi;

Thanks for the exact question.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2013-04-05 05:27:16

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,211
Website

Re: Bayes' theorem problem

But I wrote the same!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#13 2013-04-05 05:29:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

I know but it is good to check.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#14 2013-04-05 18:15:36

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

Whoops, a mistake in my previous attempt, I wasn't considering the probabilities for wrong answers!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#15 2013-04-05 19:11:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,211
Website

Re: Bayes' theorem problem

That is correct! Thanks

Let me see..


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#16 2013-04-05 19:16:25

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

You're welcome.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#17 2013-04-05 22:46:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Hi gAr;

Very good! One question, how do you figure what P(B|A) is?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#18 2013-04-05 23:51:06

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

Hi bobbym,

Thanks!
I tried to figure it out using a tree. Only the red leaves are considered for calculating our answer.

how do you figure what P(B|A) is?

Did you mean the probability that answers are the same, given that both are correct?
It must be definitely 1, since they can't have two different correct answers!

View Image: tree.png

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#19 2013-04-06 00:06:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Hi gAr;

I got confused over the wording of the problem and now I can not even see what I was confused about...

What does S stand for?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#20 2013-04-06 00:18:22

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

S stands for "same answer"


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#21 2013-04-06 00:25:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Hi;

Okay, just wanted to make sure I could understand it. Thanks for the help.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#22 2013-04-06 00:31:46

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Bayes' theorem problem

You're welcome.
I found that tree diagrams does a better job than remembering the bayes' formula, it's of great help for conditional probability problems.
We only need to select the nodes of interest, then we are done!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#23 2013-04-06 00:42:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

I have thought about treeing them for a while but I must have always left one or two out because I never got the right answer.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#24 2013-04-06 01:39:59

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,211
Website

Re: Bayes' theorem problem

Will you please make it clear to me?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#25 2013-04-06 01:52:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,420

Re: Bayes' theorem problem

Hi Agnishom;

The tree red nodes represent the denominator.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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